SOLUTION: a chemist needs 12 gallons of a 20% acid solutions. The solution is to be mixed from three soultions whose concentration are 10%, 15%, and 25%. How many gallons of each solution wi

Question 1129163: a chemist needs 12 gallons of a 20% acid solutions. The solution is to be mixed from three soultions whose concentration are 10%, 15%, and 25%. How many gallons of each solution will satisfy each conditions?

Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39628) (Show Source): You can put this solution on YOUR website!
Intended result is 20%, and no specified relationships among the three possible starter concentrations of 10%, 15%, 25%. Infinite possible combinations.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a chemist needs 12 gallons of a 20% acid solutions.
The solution is to be mixed from three solutions whose concentration are 10%, 15%, and 25%.
How many gallons of each solution will satisfy each conditions?
:
.10a + .15b + .25c = .20(12)
Since we have 3 unknowns here, lets assume we have 2 gal of 10% solution
That leaves 10 gal of the other two solutions
let b = amt of b solution
and
(10-b) = amt of c solution
Now our equation
.10(2) + .15b + .25(10-b) = .20(12)
.2 + .15b + 2.5 - .25b = 2.4
.15b - .25b + 2.7 = 2.4
-.10b = 2.4 - 2.7
-.10b = -.3
b = .3/-.1
b = 3 gal of the 15% solution
then
10 - 3 = 7 gal of the 25% solution
"How many gallons of each solution will satisfy each conditions?
2 gal 10%, 3 gal 15%, 7 gal 25% solutions
:
I'm sure there are other values for these solutions that will work

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